Great Push-Up Routine

I had a teacher in high school who was ex-military and NSA, and he gave me this great regimen that works like crazy.
Basically, you do a certain number of push-ups within an hour one day, then you do that number over the course of a whole day the next. You do this for ten days, without doing other arm exercises (i.e., chin-ups, lifting weights), and then rest for two days. After you've rested your arms, you will be able to do many more consecutive push-ups than you could before.

Before I first did this, I could do about 40 push-ups consecutively. After my first time doing this routine, I could drop and do 65. Nowadays, I can drop and do about 80.
When I first did it, my number was 250. So:
A day: 250 push-ups in an hour (25 every five minutes is how I like to do it)
B day: 250 push-ups in a day (25 about every 30 minutes)
More recently:
A day: 420 push-ups in an hour (35 every five minutes)
B day: 420 push-ups in a day (35 every 30 minutes)

If you're a 90-pound weakling, start off with 100.
A day: 100 push-ups in an hour (10 every 5 minutes)
B day: 100 push-ups in a day (10 every 30 minutes)

Try this routine out, with whatever number you can, for ten days, rest for two days. After this, you'll definitely have more muscular endurance.

Of course, this should be done so as to fit in with martial arts training and cardio work.

Well, it's not as though you're going to get injured during the program, but it's more the balance of internal vs. external rotation strength, and how this is going to create an imbalance of internal rotational strength and neglect external rotational strength. It's why shoulder injuries are so common among men in the 40s who resistance train, because they have a much higher volume of pushing compared to pulling in their training.

True. And I certainly wouldn't advocate this as the only type of exercise one should do. I actually recently typed something in a CMA thread in which I said that I like to switch up every two weeks or month.
I like to spend two weeks/month/whatever doing this routine, then the next period of time lifting weights.
So, of course, I also like chin-ups, rows, lat pull-downs, and even bicep curls.

But this routine definitely helps break through plateaus when it comes to push-ups. It's also a nice supplement to help with any weight press.

I can imagine that, I'm just wondering what you'd advocate as a means of balancing this routine for someone that wishes to follow it. This routine is very laid out and specific, and I was curious if you had something of a similar nature for a balance.

Basically, I drop and do push-ups, then do an ab exercise (for the first 5 days, crunches, now it's waist twists) for the same number. After six sets of those, I do chin-ups, then do squats (no weights). I do six sets of those.

Since I haven't done this before, I'm not as sure of the results as I am of the push-up routine. I don't feel quite as exhausted, and my push-ups may not be improving so much, but I do feel my chin-ups improving and I am regaining some of the leg muscular endurance that I seem to have lost.

I'm not advocating bodyweight only for any extended period of time. I just think it's a good idea to do different things at different times, and I have personally found bodyweight exercises (particularly this exact push-ups routine) to be quite helpful.
And, of course, they are especially helpful when traveling or on vacation or such. Whenever I visit relatives for extended periods of time, I usually do this and I find it to be rigorous and helpful.

As for the shoulder injuries, once again I'm not saying don't EVER do pulling exercises. I'm a big fan of the row and chin-ups. I was just offering up a particular routine that has given me greater muscular endurance and helped me become more fit.

The reason the initial push-up program doesn't include any pulling is simply because it is so exhaustive that any other arm exercises like chin-ups or bicep curls just hurt. I remember the first time I did it, I tried doing bicep curls afterward (foolishly ignoring my teacher's warning) and I just felt like I was injuring myself.

Because I am simply weak. My leg strength/endurance seems to have been diminished from not hitting the gym in while. Anyone else could (probably should) certainly do it with some free weights. But this is also more about endurance than raw strength, so I myself will just be increasing the number of reps in the future, not adding weights.